Problem: Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: 

  * Aij = Aji, for all i, j (1 ≤ i, j ≤ n); 
  * Bij = - Bji, for all i, j (1 ≤ i, j ≤ n); 
  * Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n). 



Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij (0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix W in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

2
1 4
3 2


Output

1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000


Input

3
1 2 3
4 5 6
7 8 9


Output

1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long moda = (1ll << 55) + 3;
long long modb = (1ll << 55) + 772347;
inline void print(char pt) { printf("%c\n", pt); }
inline void print(int pt) { printf("%d\n", pt); }
inline void print(long long pt) { printf("%I64d\n", pt); }
inline void print(double pt) { printf("%.10f\n", pt); }
inline void print(char pt[]) { printf("%s\n", pt); }
inline void print() { printf("\n"); }
inline void scan(int &pt) { scanf("%d", &pt); }
inline void scan(char &pt) { scanf("%c", &pt); }
inline void scan(long long &pt) { scanf("%I64d", &pt); }
inline void scan(double &pt) { scanf("%lf", &pt); }
inline void scan(char pt[]) { scanf("%s", pt); }
long long extend_gcd(long long a, long long b, long long &x, long long &y) {
  if (a == 0 && b == 0) return -1;
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extend_gcd(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
long long mod_reverse(long long a, long long MOD) {
  long long x, y;
  long long d = extend_gcd(a, MOD, x, y);
  if (d == 1)
    return (x % MOD + MOD) % MOD;
  else
    return -1;
}
void fail() {
  print(-1);
  exit(0);
}
int n, m;
double w[200][200];
double a[200][200];
double b[200][200];
int main() {
  scan(n);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      scan(w[i][j]);
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      a[i][j] = (w[i][j] + w[j][i]) / 2;
      print(a[i][j]);
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      b[i][j] = w[i][j] - a[i][j];
      print(b[i][j]);
    }
  }
  return 0;
}